Perhaps I am doing it the wrong way, but I have a table with 3 tabulars arranged within minipage each, such that I end up with 3 tables side by side. Each table only has 2 columns: 1 for text and one has includegraphics. I am trying to vertically align text in the first column to be in the middle of the cell.

and replace m by C in the column definitions of the tabulars of the code above. The result is then:

Two last note:
- I've replaced the references to \columnwidth in the width of the column definitions by set values. References to \columnwidth would not be appropriate nor working / constant here (see the answer to Difference between \textwidth, \linewidth and \hsize to understand why).
- In your code, the minipages are not necessary at all.